The cosmic ray (CR) flux, as well as the hydrogen flux into the atmosphere of an exoplanet, can change the composition of said atmosphere. Here, we present the CR and hydrogen flux above the atmosphere. To do so, we study the 3D multi-fluid magentohydrodynamic (MHD) structure of astrospheres. We aim to discuss the shock structure of the stellar wind of LHS 1140 using four different models: hydrodynamic (HD) and ideal MHD single-fluid models, as well as multi-fluid models for both cases, including a neutral hydrogen flow from the interstellar medium (ISM). The CR flux in a multi-fluid model and the ionization rate in an exoplanetary atmosphere are also presented. The astrosphere is modeled using the 3D Cronos code, while the CR flux at LHS 1140b is calculated using both a 1D and a 3D stochastic Galactic CR (GCR) modulation code. Finally, the atmospheric ionization and radiation dose is estimated using the AtRIS code. It is shown that the 3D multi-fluid positions of the termination (TS) differ remarkably from those found in the 3D ideal-single fluid HD case. CR fluxes computed using a 1D approach are completely different from those calculated using the 3D modulation code and show an essentially unmodulated spectrum at the exoplanet in question. Utilizing these spectra, ionization rates and radiation exposure within the atmosphere of LHS 1140 b are derived. It is shown that the multi-fluid MHD TS distances differ remarkably from those of other models, especially from an analytic approach based on ideal single-fluid HD. The TS, astropause, and bow shock distances must be taken from the 3D multi-fluid MHD model to determine the CR fluxes correctly. Moreover, because of the tiny astrosphere, the exoplanet is submerged in the neutral hydrogen flow of the ISM, which will influence the exoplanetary atmosphere. A 3D approach to GCR modulation in astrospheres is also necessary to avoid unrealistic estimates of GCR intensities. Since atmospheric chemistry processes, and with that, the derivation of transmission spectra features and biosignature information, strongly depend on atmospheric ionization, our results highlight that reliable GCR-induced background radiation information is mandatory, particularly for inactive cool stars such as LHS 1140.
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